How do I do this simple problem?

[Centurion]

Okay.

((2rad3)/3) x ((rad3)/2)

How do you multiply 2rad3 by rad3?

 

[wjm11]

((2rad3)/3) x ((rad3)/2)

How do you multiply 2rad3 by rad3?

http://www.purplemath.com/modules/radicals.htm

 

[Centurion]

Could someone answer my question, please?
I appreciate the link though. It is very insightful.

 

[Deleted member 4993]

Rewriting the hint above in LaText:

$\displaystyle \sqrt{x} \ * \ \sqrt{x} \ = \ x$

$\displaystyle A \ * \ \sqrt{x} \ * \ \sqrt{x} \ = \ A \ * \ x$

Then the answer to the question

How do you multiply 2rad3 by rad3?

is

The same way you multiply 2*3 by 3

 

[Deveno]

another way to look at it is:

$\displaystyle \sqrt{x} = x^{1/2}$, so

$\displaystyle (a\sqrt{x})(b\sqrt{x}) = (ab)(\sqrt{x}\sqrt{x})$

$\displaystyle = (ab)(x^{1/2})(x^{1/2}) = (ab)(x^{(1/2 + 1/2)}) = (ab)x^1 = (ab)x$

using the familar "laws of exponents".

for the time being, it's best to restrict such use (of exponent laws) to "rational exponents" and "non-negative x", for reasons which are too far off-topic to go in to.